why does loop-cut-and-slide ignore some faces but not others?
First you should fix the mesh. This might be part of the problem.


Remove the double geometry, W -> Remove Doubles
Select all geometry, A
Recalculate the normals, Ctrl N


Does the problem persist? If so you might have to do some manual cleanup. The problem might be that you have ngons in your mesh.


To see if you bad geometry go into vertices mode and Shift Ctrl Alt M to select all non-manifold geometry. If something was selected near at the place where the edge loop does not work that also indicates a problem, if not there still might be a problem
Also to select all n-gons you can do Select -> Select Faces by Sides. Set the number to 4 and the type to Greater Than If you have n-gons they will now be selected.
Go into vertices mode, in face mode it is harder to stop ngons
If you see that there are random vertices along the edges you should delete them, x -> dissolve vertices.


An example of a random vertex along an edge